Probing 3D magnetic fields using starlight polarization and grain alignment theory

Polarization of starlight induced by dust grains aligned with the magnetic field (hereafter B-field) is widely used to measure the two-dimensional B-fields projected onto the plane-of-sky. Here, we introduce a new method to infer three-dimensional B-fields using starlight polarization. We show that the inclination angle or line-of-sight (LOS) component of B-fields can be constrained by the starlight polarization efficiency from observations, the alignment degree provided by the magnetically enhanced radiative torque (MRAT) alignment theory, and the effect of B-field tangling. We first perform synthetic observations of starlight polarization of magnetohydrodynamic (MHD) simulations of a filamentary cloud with our updated POLARIS code incorporating the modern MRAT theory. We test the new technique with synthetic observations and find that the B-field inclination angles can be accurately determined by the synthetic starlight polarization efficiency once the effects of grain alignment, dust properties, and B-field fluctuations are well characterized. The technique can provide an accurate constraint on B-field inclination angles using optical polarization in low-density regions $A_{\rm V}< 3$ with efficient MRAT alignment, whereas the technique can infer further to high-density regions with significant alignment loss at $A_{\rm V} \sim 8 - 30$ by using near-infrared polarization. Our new technique unlocks the full potential of tracing 3D B-fields and constraining dust properties and grain alignment physics on multiple scales of the diffuse interstellar medium and star-forming regions using multi-wavelength starlight polarization observations.